Trace formulae and inverse spectral theory for Schrödinger operators

DOI10.1090/S0273-0979-1993-00431-2zbMath0786.34081arXivmath/9310229OpenAlexW1978382686MaRDI QIDQ4275684

Barry Simon, Helge Holden, Zhongxin Zhao, Friedrich Gesztesy

Publication date: 31 January 1994

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9310229

zbMATH Keywords

inverse problemsabsolutely continuous spectrumone-dimensional Schrödinger operatorstrace formula for Hill's equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse problems involving ordinary differential equations (34A55)

Related Items (14)

The spectral theory of the vibrating periodic beam ⋮ On new trace formulae for Schrödinger operators ⋮ Traces of Sturm-Liouville operators with discontinuities ⋮ Last-passage time for linear diffusions and application to the emptying time of a box ⋮ On \(A\)-integrability of the spectral shift function of unitary operators arising in the Lax-Phillips scattering theory ⋮ Inverse nodal problem for the integrodifferential Dirac operator with a delay in the kernel ⋮ New trace formulae for Sturm-Liouville operators on the Lasso-graph ⋮ On the heat trace of schrödinger operators ⋮ Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators ⋮ The periodic Euler-Bernoulli equation ⋮ The Floquet theory of the periodic Euler-Bernoulli equation ⋮ New trace formulae for a quadratic pencil of the Schrödinger operator ⋮ Absolute summability of the trace relation for certain Schrödinger operators ⋮ Necessary and sufficient conditions for absolute summability of the trace formulas for certain one dimensional Schrödinger operators

Cites Work

• On the measure of the spectrum for the almost Mathieu operator
• Kotani theory for one dimensional stochastic Jacobi matrices
• Almost periodic Schrödinger operators. II: The integrated density of states
• Almost periodicity of some random potentials
• A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants
• The spectrum of Hill's equation
• On the inverse problem for Hill's operator
• The \(\xi\) function
• The trace formula for Schrödinger operators on the line
• Absolute summability of the trace relation for certain Schrödinger operators
• The infinite period limit of the inverse formalism for periodic potentials
• The inverse problem for periodic potentials
• HIGHER ORDER TRACE RELATIONS FOR SCHRÖDINGER OPERATORS
• Unnamed Item
• Unnamed Item

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